image texture unaligned on uv map
Exporting UV layout from Blender works fine and there are no options for the export procedure that could result in a shift of UVs so it is extremely unlikely the problem happens when exporting the UV layout.

As the UV layout is exported in a simple picture format any digital image processing software will most likely be able to read it correctly because that is a very basic operation as far as digital image processing goes so it is extremely unlikely the problem is there as well.

We are left with a few very likely possibilities - you either accidentally moved the UV map or you accidentally moved the image or the image of the UV layout. There is really little mystery here - it is very easy to accidentally click and drag an image.

You can select all the UVs (a) and hit g to move them to their correct position. You can zoom in to be precise and also use shift during the operation to increase precision.